Group analysis of the Novikov equation
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We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilation symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigate the invariant solutions.
KeywordsNovikov equation Lie symmetries Strictly self-adjointness Conservation laws Invariant solutions
Mathematics Subject Classification (2000)76M60 58J70 35A30 70G65
The authors would like to thank FAPESP, São Paulo, Brasil, and BTH, Sweden, for the support giving Nail H. Ibragimov the opportunity to visit IMECC-UNICAMP, where this work was initiated. Yuri Bozhkov would also like to thank FAPESP and CNPq, Brasil, for partial financial support. Igor Leite Freire is thankful to IMECC-UNICAMP for gracious hospitality, UFABC and FAPESP (Grant No. 2011/19089-6) for the financial supports. N. H. Ibragimov’s work is partially supported by the Government of Russian Federation through Resolution No. 220, Agreement No. 11.G34.31.0042.
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